>From what I remember of my astronomy course, it is a general principle that
an object which varies over a time scale t can't be much larger than t*c
in size. Or, putting it the other way, an object which is t*c in size can't
be seen to vary strongly with time scales much less than t.
The reason is that, generally, the radiation will come to us from all over
the object, or at least all over the side of the object facing us. The
distances to the different parts of the object, assuming it is t*c in size,
will therefore vary by around t*c/2 between the closest and farthest parts
of the object that we see. We are really dealing with orders of magnitude
here so that is effectively about the same as t*c.
Now, if the object suddenly and uniformly changes its brightness,
we will still see the brightness to change over a period of about t.
First the closest part of the object will brighten, then the farther
parts, and so on. There will be a difference in time of about t from
when we see the object start to brighten until the brightness change is
complete.
You can imagine geometries where this might not happen; for example, if
the object were plane shaped, and we were face on to it, and the whole
thing changed at once, then it could change suddenly in brightness even
though the plane was larger than t*c. However this requires unusual
geometry, and in that case there should be a range of objects with
varying time scales but otherwise similar behavior (where the geometry
happens to be more typical), and I don't think that is the case with GRBs.
I'm not sure how Carl Feynmann got those incredible numbers about the
energy density within the GRB. Presumably you look at its (huge) distance
from us, look at the energy we saw, assume that it was radiating that
much energy in all directions, and get a whole lot of energy. Then the
whole event takes a few seconds, so it has to have all originated in a
small volume, and things get pretty hard to explain.
One thing I was thinking was that the radiation could perhaps be going
out in a tight beam. GRB's would actually be much more common than we
see, but most of them miss us. However you would still have extremely
high energy densities unless the beam is super tight. Also the fact
that something was visible for hours or days afterwards doesn't sound
right for a tight-beam phenomenon.
Hal